This paper examines the effects of monetary policy in an optimizing two-country model in which monopolistically competitive firms set their prices in advance, so that the prices are sticky. The main findings of this paper are that there occurs an instantaneous depreciation of the exchange rates through a countercyclical response of a markup when there is a positive home monetary shock. The paper shows that the sticky price model cannot resolve the forward premium puzzle. The degree of depreciation depends on the degree of price stickiness as real variables become more volatile with stronger price stickiness. Finally, the nominal exchange and real exchange rates move very closely as in data when there is a substantial degree of price rigidity.